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Usage guidance, also known as a tag wiki excerpt, is a short blurb that describes when and why a tag should be used on this site specifically.

A polynomial is an expression constructed by a finite linear combination of positive integer powers of a number of variables. If there is only one variable, the polynomial is called univariate, otherwise multivariate.

Polynomials appear in many fields of mathematics and physics and many have been named after mathematicians who have discovered some of their properties (Legendre, Chebychev, Laguerre, Jacobi, ...).

Finding the roots of a polynomial (i.e. the values of the variables for which the polynomial expression evaluates to exactly zero) is an ever-recurring problem in mathematics and physics.